Answer: 23 years.
Step-by-step explanation: The labor productivity grows 3% per year, then the rate of growing is 1 + 0.03 = 1.03.
The equation to caclulate the years is:
[tex]y = y_{0}.(1.03)^{t}[/tex]
To double: [tex]y = 2y_{0}[/tex]
Substituing:
[tex]2y_{0} = y_{0}.(1.03)^{t}\\(1.03)^{t} = 2\\ln1.03^{t} = ln2\\t = \frac{ln2}{ln1.03}\\ t = 23[/tex]
To double the standard of living, it will take 23 years.
the length of rectangle exceeds its breadth by 4 cm if the length and breadth is increased by 3 cm the area of the new rectangle will be 81 squares more than that of the given rectangle find the length and breadth of the given rectangle check your solution.
Answer:
The length and breadth are 14 cm and 10 cm
PLZ HELP, AND PLZ EXPLAIN
Answer:
C
Step-by-step explanation:
To make it easy let's start by organizing our information :
AC=12 AND BD=8 ABCD is a rhombus K and L are the midpoints of sides AD and CD we notice that the rhombus ABCD is divided into four right trianglesWhat do you think of when you hear a right triangle ?
The pythagorian theorem !AC and BD are khown so let's focus on them .
If we concentrated we can notice that AB and BD are cossing each other in the midpoints . why ?
Simply because they are the diagonals of a rhombus .
ow let's apply the pythagorian theorem :
(AC/2)² + (BD/2)² = BC² 6²+4²=52BC²= 52⇒[tex]\sqrt{52}[/tex]=BCNow we khow that : AB=BC=CD=AD=[tex]\sqrt{52}[/tex]
This isn't enough . Let's try to figure out a way to calculate the length of KL wich is the base of the triangle
KL is parallel to AC k is the midpoint of AD and L of DCI smell something . yes! Thales theorem
KL/AC=DL/DC=DK/AD WE4LL TAKE OLY ONE KL/12=[tex]\sqrt{52}[/tex]/2*[tex]\sqrt{52}[/tex] KL/12=1/2⇒ KL=6Now we have the length of the base kl
Now the big boss the height :
notice that you khow the length of KL BD crosses kl from its midpoint and DL = [tex]\sqrt{52}[/tex] /2What I want to do is to apply the pythgorian thaorem to khow the lenght of that small part that is not a part of the height of the triangle . I will call it D
DL²=(KL/2)²+D²52/4= 9+ D² D² = 52/4-9 +4 SO D=2now the height of the trigle is H= BD-D= 8-2=6
NOw the area of the triangle is :
A=(KL*H)/2 ⇒ A= (6*6)/2=18THE ANSWER IS 18 SQ.UN
8.(2 + 3)2 - 42
What is the answer
Answer:
-34
Step-by-step explanation:
(2+3)2-42
open the bracket, multiply 3 ×2 to open it
it will be, 2+6-42
+8-42= -34
What does C represent in this equation (-9c)-4=-25
Answer:
[tex]c=2\frac{1}{3}[/tex]
Step-by-step explanation:
[tex](-9c)-4=-25\\(-9c)=-21\\9c=21\\c=21/9=2\frac{1}{3}[/tex]
the value of x is and the value of y is
Answer:
x = 60, y = 50
Step-by-step explanation:
60 + 50 = 110 + 70 = 180.
50 + 70 = 120 + 6 = 180.
Therefore 50 + 70 + x = 60
Therefore 70 + 60 + y = 50
Answer:
x = 60°y = 50°Step-by-step explanation:
Angles in a triangle add up to 180 degrees.
x + 70 + 50 = 180
x + 120 = 180
x = 60
The other triangle's missing angle:
180 - 60 - 50 = 70
Angles on a straight line add up to 180 degrees.
70 + x + y = 180
We know the value of x.
70 + 60 + y = 180
Solve for y.
130 + y = 180
y = 180 - 130
y = 50
which equation describes the same line as y-3=-1(x+5)
Answer:
y = -x - 2
Step-by-step explanation:
y-3=-1(x+5)
Expand.
y - 3 = -1x - 5
Add 3 on both parts.
y - 3 + 3 = -1x - 5 + 3
y = -1x - 2
The legs of a right triangle are 3 units and 5 units. What is the length of the hypotenuse? Round your answer to the nearest hundredth. 4.00 units 2.83 units 5.83 units 8.00 units
Answer:
5.83units
Step-by-step explanation:
from Pythagoras theorem;
a^2=b^2+c^2
where a is the hypotenuse,b is the opposite and c is the adjacent
b=3 and c=5
a^2=3^2+5^2
a^2=9+25
a^2=34
find the square root of both sides,
√a^2=√34
a=5.83units
Answer:5.83
Step-by-step explanation:
While watching a football game, Jeevan decided to list yardage gained as positive integers and yardage lost as negative integers. After these plays, Jeevan recorded 14, –7, and 9. What was the net gain or loss?
Answer:
It was a gain, specifically 16
Step-by-step explanation:
14 + (-7) = 7
7 + 9 = 16
Please tell me if I'm wrong.
Please answer ASAP Amanda used 24 grams of paint to paint a wooden cube. When it dried, she cut the cube into 8 equal cubes. How many more grams of paint does Amanda need to paint the unpainted surfaces of the 8 cubes?
Answer:
24 g
Step-by-step explanation:
hello,
The big cube is compose by the 8 small cubes.
Because of the symmetry we can check what's happening to one of this small cube.
As Amanda has already painted the big cube it means that the same cube has 3 faces painted, so 3 faces are left unpainted. only 50 % is painted.
so Amanda need 24 grams to paint the unpainted surfaces of the 8 cubes.
hope this helps
Amelia rented a DVD and it was due to be returned on 26 November. She actually returned it to the shop on 12 December. The rental shop applies a fine of 9p for every day the DVD is overdue. Work out the total fine paid by Amelia. give your answer in £
Answer:
£144
Step-by-step explanation:
DVD to be due on 26 of November
She returned it to the shop on 12 of December
Extra days:
November has a total of 30 days less 26 days=4 extra days
December 12 =12 extra days
Total extra days =4+12=16 days
Fine per day=£9
Total fine paid by Amelia=£9*16
=£144
Marcel used the multiplication table below to determine that 72:24 is equivalent to 6:18. A multiplication table. In the row labeled 3, the numbers 3, 6, 9, 12, 15, 18, 21, 23, and 27 are highlighted. In the row labeled 9, the numbers 9, 18, 27, 36, 45, 54, 63, 72, and 81 are highlighted. What was Marcel’s error? Marcel did not look at the correct rows in highlighted columns. Marcel did not choose numbers from the highlighted columns. Marcel did not put the first and second terms in the same order. Marcel did not use numbers from the same row to create each ratio.
Answer:
The correct option is;
Marcel did not put the first and second term in the same order
Step-by-step explanation:
From the multiplication table the equivalent ratios of two numbers can be found given that the two numbers have the same factors which is true if the numbers are on the same column in the multiplication table
Therefore, having the numbers ratio presented in the form 72:24 which are on the row labelled 3 and the row labelled 9, we have that the 72 is on row 9 while the 24 is on row 3, for which on the second column, we have 6:18
However the ordering of the ratio gives the value on the 9th column first before the value on the 3rd column, so that the correct result should be 18:6
The error was that Marcel did not put the first and second term in the same order.
Answer:
C
Step-by-step explanation:
-5(p+3/5)=-4 solve for p
Answer:
p=1/5
remove brackets
-5p-3=-4
move constant to right
-5p=-4+3
-5p=-1
divide both sides by -5
p=1/5
Answer:
1/5
Step-by-step explanation:
We can use solving for variables here.
-5(p+3/5)=-4
-5p+-3=-4
p=1/5
Hiiii someone please help me I'm confused please helppp
If the length of the bases of right triangle GHI are 9 units and 15 units respectively, what is the length of the hypotenuse of GHI?
Answer:
17.5 units
Step-by-step explanation:
a² + b²= c²
9² + 15² = c²
81 + 225 = c²
c² = 306
c = √306
c = 17.5
The slope of a line is -1/3
and the y-intercept is 10/3.
What is the equation of the line written in general form?
O 10x + 3y - 1 = 0
OX + 3y + 10 = 0
Ox + 3y - 10 = 0
Answer:
x + 3y - 10 = 0.
Step-by-step explanation:
Since the slope is -1/3 and the y-intercept is 10/3, we can have a slope-intercept form of y = -1/3x + 10/3.
Multiply all terms by 3
3y = -x + 10
Add x to both sides
x + 3y = 10
Subtract ten from both sides
x + 3y - 10 = 0.
Hope this helps!
Answer:
x+3y -10 =0
Step-by-step explanation:
The slope intercept form is
y = mx+b where m is the slope and b is the y intercept
y = -1/3x + 10/3
Multiply each side by 3 to get rid of the fraction
3*y = 3*(-1/3x + 10/3)
3y = -x + 10
Add x to each side
x+3y = 10
Subtract 10 from each side
x+3y -10 =0
The general from is
Ax + By +C = 0 where A is a positive integer and B and C are integers
Help with this plz! Please❤️
Answer:
1) Qs= 24.4 cm
2) Perimeter= 72.8 m
Step-by-step explanation:
1).let qs= qos
Op is the height of the the triangle
Op= ,6.8cm
Angle ops = 180-(90+50)
Angle ops = 180-140
Angle ops = 40
Os/sin ops= op/sin pso
Os/sin 40= 6.8/sin 50
Os = sin 40(6.8)/sin50
Os= 0.6428(6.8)/0.7660
Os= 5.71
Angle oqp = 180-(90+70)
Angle oqp = 180-160.
Angle oqp = 20
Oq/sin qpo = op/sin oqp
Oq/sin 70=6.8/sin 20
Oq= sin70(6.8)/sin20
Oq= 0.9397(6.8)/0.3420
Oq= 18.68
Qs= os +oq
Qs= 5.71+18.68
Qs= 24.39
Qs= 24.4 cm
2). The other angle of the triangle
=180-90-53
= 37
Sin90 = 1
Let the length and breadth be x and y
X /sin 53 = 26
X= 26(sin53)
X= 26(0.7986)
X= 20.7636
Y/sin 37 = 26
Y= 26(0.6018)
Y= 15.6468
Perimeter= 2(x+y).
Perimeter= 2( 20.7636+15.6468)
Perimeter= 2(36.4104)
Perimeter= 72.8208 m
Perimeter= 72.8 m
find the equation of the line shown
Answer:
From the graph, the y-intercept is 9 and the slope is -1 so the equation is y = -x + 9. We know the slope is -1 because when x goes up by 1, y decreases by 1.
Step-by-step explanation:
When we know both the x- and y-intercepts of a line, we can conveniently use the intercept form.
Let
A=x-intercept=9
B=y-intercept=9
the intercept form of the equation is therefore
x/A + y/B =1
substituting numerical values,
x/9 + y/9 =1 ..........................(1)
Factoring the identical denominators
(x+y)/9 = 1
Cross multiply
x+y = 9 ...............................(2)
Both (1) and (2) are valid forms of equation of the given line.
The graph of y=h(x)y=h(x)y, equals, h, left parenthesis, x, right parenthesis is a line segment joining the points (1,9)(1,9)left parenthesis, 1, comma, 9, right parenthesis and (3,2)(3,2)left parenthesis, 3, comma, 2, right parenthesis. Drag the endpoints of the segment below to graph y=h^{-1}(x)y=h −1 (x)y, equals, h, start superscript, minus, 1, end superscript, left parenthesis, x, right parenthesis.
Answer:
End points of the this segment are (9,1) and (2,3).
Step-by-step explanation:
The given function is
[tex]y=h(x)[/tex]
End points of the this segment are (1,9) and (3,2).
If a function is defined as
[tex]f=\{(a,b),a\in R,b\in R\}[/tex] then
[tex]f^{-1}=\{(b,a),a\in R,b\in R\}[/tex]
It means, we have to interchange x and y-coordinates of the end points.
So, end points of the this segment are (9,1) and (2,3).
Plot these point and join them by a line segment.
The inverse of the function will be a line segment joining the points (9,1) and (2,3). See the graph.
Given information:
The function y=h(x) is a line segment joining the points (1,9) and (3,2).
So, the endpoints of the function y=h(x) can be written as,
[tex]y=h(x)=\{(1,9),(3,2)\}[/tex]
The inverse of a function is simply the opposite relation. In the inverse, the range and domain interchange themselves.
So, the inverse of the given function can be written as,
[tex]y=h^{-1}(x)=\{(9,1),(2,3)\}[/tex]
Refer to the graph of the function for more details.
For more details, refer to the link:
https://brainly.com/question/10300045
Help pls I will give BRAINLY
Answer: The missing length is 16/3
Step-by-step explanation:
First, you have to find the proportional value between the two lengths on the first figure and the two lengths on the second figure.
The first figure’s lengths are 8 and 9, so the shorter length is 8/9 of the longer length.
Now apply the same proportional value to the second figure.
6 * 8/9 = 48/9
48/9 = 16/3
Find the value of x in each case:
Answer:
25.5°
Step-by-step explanation:
the sum of angle NMR and MRS is 180, so
2x + x + x + 78 = 180
4x = 180 - 78
4x = 102
x = 102/4 = 25.5°
(ii) The scale 1 cm represents 50m can be written in the form 1:k.
Find the value of k.
k=
[1]
Answer:
k = 50
Step-by-step explanation:
The scale 1 cm represents 50m
It means that 1 cm length of pictorial representation of any obejct is equivalent to 50m in reality.
In scale terms it can be represented in ratio form of a:b
where
a is the length of picture and b is actual length
here length of pictorial representation is 1 cm
and 50m is actual length
thus scale will be 1:50
But is given that The scale 1 cm represents 50m can be written in the form 1:k.
1:50 is same as 1:k
thus
1:50 = 1:k
we know that in ratio
if a:b = c:d
then
a= c and b = d
Thus,
k = 50 Answer
→Can someone help me←
Answer:
B.
Step-by-step explanation:
When written as proportions, the ratios of oranges to cups of juice are always equal.
Winnie has 17 red balloons, 33 white balloons, 65 green balloons, and 83 chartreuse balloons. With no regard to color, Winnie gives each of her 8 nearest and dearest friends some balloons. Each friend gets the same number of balloons and she hands out as many balloons as possible. How many balloons does Winnie end up keeping for herself?
Answer:
6
Step-by-step explanation:
17 + 33 + 65 + 83 = 198
198/8 = 24.75
To give the highest possible number, but the same number of balloons to each person, she gives 24 balloons to each one.
24 * 8 = 192
198 - 192 = 6
She gives away 192 balloons and keeps 6.
2^5×5×11 and 2^3×5^2×7
Answer:
1. 1760
2. 1400
Step-by-step explanation:
2^5 = 32
32 × 5 = 160
160 × 11 = 1760
2^3 = 8
5^2 = 25
8 × 25 = 200
200 × 7 = 1400
I NEED HELP ASAP!!! LIKE RIGHT NOW RIGHT NOW ILL GIVE THE MOST BRAINLIEST
Answer:
see below
Step-by-step explanation:
We know that the center is (0,0) and the radius is |3 - 0| = 3.
Standard form of a circle: (x - h)² + (y - k)² = r² where (h, k) is the center and r is the radius. Plugging in h = 0, k = 0 and r = 3 gives us x² + y² = 9.
Answer:
See below.
Step-by-step explanation:
The equation for a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h,k) is the center and r is the radius.
From the graph, we can see that (0,0) is the center.
Thus, h=0 and k=0:
[tex]x^2+y^2=r^2[/tex]
From the graph, we can also see that the radius is 3 as (-3,0) and (3,0) are points on the circle.
Thus, r=3, and r^2=9.
The equation is:
[tex]x^2+y^2=9[/tex]
Classify the following triangle. Check all that apply.
Answer:
B and C
Step-by-step explanation:
Since all of it's sides are unequal, it is a scalene triangle.
It has 1 obtuse angle, so it is an obtuse angled triangle.
A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 10 cubic centimeters. Find the radius of the cylinder that produces the minimum surface area. (Round your answer to three decimal places.)
Answer:
1.619
Step-by-step explanation:
We have the formulas for the volume of the sphere and the cylinder:
Vs = (4/3) * pi * (r ^ 3)
Vc = pi * h * (r ^ 2)
Thus:
(4/3) * pi * (r ^ 3) + pi * h * (r ^ 2) = 10
Now, the formula for the surface area of the cylinder and sphere are:
As = 4 * pi * (r ^ 2)
Ac = 2 * pi * r * h + 2 * pi * r ^ 2
Using this equation for the total surface area of the solid, we can see that as "h" increases, so will the surface area. Therefore, the smallest surface area will occur at h = 0.
Thus:
(4/3) * pi * (r ^ 3) + pi * 0 * (r ^ 2) = 10
(4/3) * pi * (r ^ 3) = 10
r ^ 3 = 4 * 10 / (3 * 3.14)
r ^ 3 = 4.24
r = 1.619
so the radius is 1.619
Simplify expression 1/4 •3(8a-5b-4)-(4a+1)+4b
Answer:
(8a+b-16)/4
Step-by-step explanation:
1/4×3(8a-5b-4)-(4a+1)+4b
Simplify:
-4a-1+4b+1/4×3×8a-1/4×3×5b-1/4×3×4
=1/4xax24-4a-1/4bx15+4b-1/4×12-1
=1ax24/4 -4a - 1bx15/4 +4b -1×12/4 -1
=ax24/4 -4a -bx15/4 + 4b -12/4 -1
= -4a + 24a/4 + 4b - 15b/4 -1 -3
= -4a + 6a + 4b - 15b/4 - 4
= 2a + 4b - 15b/4 - 4
= 8a + 16b - 15b - 16 / 4
= (8a + b - 16) / 4
= 8a + b - 16 / 4
What value of x is in the solution set of 9(2x + 1) < 9x – 18?
Ο Ο Ο Ο
-2
Answer:
x < -3
Step-by-step explanation:
9(2x + 1) < 9x – 18
18x +9 < 9x – 18
-9x -9x
9x +9 < – 18
-9 -9
9x < – 27
÷9 ÷9
x < -3
HOPE THIS HELPS:)
Find the relative size T of the shock wave of earthquakes with magnitude 8.3, as measured on the Richter scale (Answer in scientific notation, rounded to the nearest hundredth).
Answer:
199,526,231.50
Step-by-step explanation:
Mathematically, we use the Logarithmic relation below;
R = Log T
8.3 = Log T
T = (Log)^-1 8.3
T = 199,526,231.49688828
Which to the nearest hundredth is T = 199,526,231.50
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Find the following expression by multiplying.
(a + b)3
Answer:
[tex]a^3+3a^2b+3ab^2+b^3[/tex]
Step-by-step explanation:
If have [tex](a+b)^3[/tex], we can solve this as:
[tex](a+b)(a+b)(a+b)[/tex]
So, applying distribution with the first two factors and simplifying, we get:
[tex](a^2+ba+ab+b^2)(a+b)\\(a^2+2ab+b^2)(a+b)[/tex]
Then, multiplying both expressions and simplifying again, we get:
[tex]a^3+a^2b+2a^2b+2ab^2+b^2a+b^3\\a^3+3a^2b+3ab^2+b^3[/tex]